The present invention in general relates to a technology for obtaining the relation between data values widely used in industrial fields and extracting a significant result for producing an industrially predominant result.
In a semiconductor fabrication process, operations for finding out a yield-deterioration factor as quick as possible are performed in accordance with the history of a device used in a fabrication stage, test results, design information, and various measured data values in order to improve the yield.
Particularly, in the case of development of a new product or review of an existing fabrication process, it is important to extract variable information or regularity hidden in data from the above various original data groups in order to make a data analysis efficient and high reliable. Moreover, by integrating and studying the extracted information and regularity, it is possible to find a knowledge not easily found by an engineer and effectively use the knowledge to find a yield-deterioration factor. Data mining is a data analyzing method for realizing the above mentioned, particularly utilize in finance and circulation fields. Because these industrial fields use a large quantity of data, it is suitable to apply the data mining to the industrial fields.
FIG. 1 is a conceptual illustration showing a general data analyzing method to which data mining is not applied. In the case of the general data analyzing method, individual original data values extracted from databases 2a, 2b, . . . of an original data group 1 are directly analyzed by an analyzing tool group 3. According to the analysis result, decision making is performed. The analyzing tool group 3 includes a statistical analysis component 4a and a chart drawing component 4b. 
FIG. 2 is a conceptual illustration showing a conventional data analyzing method executed in a semiconductor fabrication process. A conventional semiconductor fabrication process uses a general data analyzing method to which data mining is not applied. An original data group 5 is provided with a data base 6a for design data, a data base 6b for process data, a data base 6c for device data, and a data base 6d for test results and the like. Analysis-object data 7 is constituted of the original data extracted from the databases 6a, 6b, 6c, and 6d. The analysis-object data 7 is processed by a data processor 8 and data 9 for low-yield factors is obtained.
The analysis-object data 7 is extracted in accordance with an analysis procedure or layer. Data to be extracted or data to be used for an analysis is decided in accordance with the past know-how, experience, and skill of each engineer. That is, a decision data is left to the discretion of an engineer who performs an analysis. Moreover, the analysis result is shown in the form of a correlation diagram, trend graph, or histogram.
In general, a device-difference analysis is performed in order to clarify a yield-deterioration factor in a semiconductor fabrication process. FIG. 3 is a conceptual illustration showing the flow of a lot in the device-difference analysis and FIG. 4 is a box and whisker chart showing the yield value of a lot in the device-difference analysis every device used. The box and whisker chart is drawn for each fabrication process. In the case of the device-difference analysis, it is extracted which device most influences the yield in each fabrication process from the data for a device used for the process of each lot. Then, a process in which a yield difference is most remarkable and a device used are identified in accordance with an obtained box and whisker chart.
However, the above device-difference analysis has a problem that extremely large man-hour is required for the analysis because the number of fabrication processes is several hundreds at present. Moreover, when a difference between devices is not clearly obtained or conditions are complexly combined, there is a disadvantage that it is sometimes difficult to determine.
Furthermore, because an analysis is progressed in accordance with the past know-how, experience, or skill of each engineer in the case of a conventional analyzing art, it cannot be avoided that the efficiency or reliability of an analysis is unavoidable. Therefore, a data analysis art is desired which makes it possible to decrease the rate depending on the know-how, experience, or skill of an engineer, effectively use study of the knowledge for efficiently executing the analysis by each analyzing tool so that there is no leak and the study result, and even evaluate the accuracy of the study result.
FIG. 5 is a schematic view showing a configuration of records used for the data analysis of the classification analysis which is one of data mining methods. Generally, in the case of a data analysis, a variable purposing searching a fluctuation cause or fluctuation pattern is referred to as a purpose variable and a variable for explaining the fluctuation of purpose variables is referred to as an explanation variable. Records 10a, 10b, . . . , 10i are divided into purpose-variable data values 11a, 11b, . . . , 11i and explanation-variable data values 12a, 12b, . . . , 12i. The efficiency or reliability of an analysis is changed depending on an object used as purpose variables or explanation variables or a type of analysis to be performed. Therefore, it is necessary to evaluate the reliability or accuracy of an analysis.
To analyze the data for the yield of a semiconductor fabrication process in many cases, a purpose variable uses a yield and a explanation variable uses the history of a device used, test results, design information, and various measured data values. To more efficiently perform an analysis and improve the reliability of the analysis, it is necessary to perform the processing for clarifying the relation between purpose variables and an explanation variables in an original data group and an existing analyzing-tool group as shown in FIG. 1.
Data mining is effective as a method for clarifying the relation between purpose variables and explanation variables. FIG. 6 is a conceptual illustration for showing a general data analyzing method to which data mining is applied. In the case of the data analyzing method to which data mining is applied, a rule file 16 is generated by an device 15 for extracting processing of features and regularities hidden in data (data mining) in accordance with individual original data value extracted from data bases 14a, 14b, . . . of an original data group 13.
Then, individual original data value extracted from the data bases 14a, 14b, . . . is analyzed by an analyzing tool group 17 in accordance with the rule file 16. Decision-making is performed in accordance with the analysis result. The analyzing tool group 17 includes, for example, a statistical analysis component 18a and a chart drawing component 18b. 
When applying data mining to a yield data analysis, an action for improving a yield is decided in accordance with a data mining result, it is determined whether to take action for that or not, or an action effect is estimated. For this, quantitative evaluation or accuracy of a data mining result is necessary.
A regression tree analysis is particularly effective among classification analyses of the data mining method. One of advantages of the regression tree analysis is that results are output as an comprehensible rule and expressed by a general language or a database language such as an SQL language. Therefore, by effectively using the reliability or accuracy of these results, it is possible to perform effective decision making or take actions in accordance with the result.
The regression tree analysis is described below. The regression tree analysis is applied to a set constituted of records comprising explanation variables showing a plurality of attributes and a purpose variable to be influenced by the explanation variable, which identifies an attribute which most influences the purpose variable and an attribute value. A rule showing the feature and regularity of data is output from a regression tree analysis engine.
The processing of the regression tree analysis is realized by repeatedly diving a set into two subsets in accordance with the attribute value of each attribute. When dividing, by assuming the sum of squares of purpose variables before divided as S0 and the sum of squares of purpose variables of two subsets after divided as S1 and S2, the attribute of a record for performing division so that xcex94S shown by the following equation (1) is maximized and the attribute value of the record are obtained.
xcex94S=S0xe2x88x92(S1+S2)xe2x80x83xe2x80x83(1)
The attribute and attribute value obtained from the above equation correspond to a branch point of a regression tree. Subsequently, the same processing is repeated for divided subsets to examine influences of an explanation variable on a purpose variable. Therefore, an explanation variable located at a higher position from a branch more strongly influences a purpose variable. Then, when the standard deviation of purpose variables of divided subsets becomes smaller than a previously designated value, branching of the regression tree stops. Thus, influences of the attribute value of each attribute on a purpose variable is identified in accordance with a regression tree diagram obtained by repeating set division in accordance with the value of xcex94S.
However, when a subject to be analyzed relates to a fabrication process such as a semiconductor, there may be more than one actual low-yield factors. Moreover, there is a case in which a factor determined as a factor having the largest significant difference in a data analysis is not true in fact. This is because only a factor regarded to be most significant at each stage of set division, that is, only a factor having the maximum xcex94S is output from a normal regression-tree-analysis engine. That is, the accuracy or reliability of an analysis is not sufficiently obtained.
On the other hand, data mining is frequently used in finance and circulation fields. Though data values used in these fields require a great number of records (e.g. POS data), most of the data values have a comparatively small number of explanation variables. However, the data obtained from a fabrication process has a large number of explanation variables though the number of records is small. Therefore, a method basically different from a conventional method is necessary for the accuracy and reliability of analysis results of data mining.
To apply data mining to the data for a fabrication process, the accuracy evaluation of data-mining results is important because fabrication conditions are changed depending on a data-mining result. Particularly, in the case of a fabrication process of device LSI products whose number of lots is small, the information for the above reliability and accuracy or for factors which may be factors from a secondary factor downward is important.
The accuracy evaluation of not only data mining but also a rule generally obtained as a classification analysis result of a multivariate analysis is performed in accordance with the following equation (2).
(Erroneous classification rate)=(Number of data values erroneously identified)/(Total number of data values)xe2x80x83xe2x80x83(2)
FIG. 7A and FIG. 7B are illustrations for explaining the accuracy evaluation of a rule. In FIG. 7A and FIG. 7B, states are shown in which the data of A group provided with triangular marks and the data of B group provided with circular marks are identified by two explanation variables X1 and X2. In the case of the classification in accordance with the linear classification function shown in FIG. 7A, the circular mark (shown by symbol 19) present at the middle of B-group data is erroneously identified as A-group data. Therefore, an erroneous classification rate becomes {fraction (1/12)}.
However, in the case of the classification in accordance with the Mahalanobis"" distance shown in FIG. 7B, every circular mark is correctly identified. Therefore, the erroneous classification rate becomes zero. It is possible to evaluate a data-mining result with the same method depending on the type of data or analysis content. However, because a data quantity is large, a method according to sampling or cross validation may be used.
In these evaluation methods, it is assumed that the attribute of each data value is completely already known and it is possible to determine whether a classification analysis result is correctly identified. However, it is impossible to identify a true state from the viewpoint of the property of process data and the accuracy evaluation according to an erroneous classification rate does not make sense.
Moreover, even if an erroneous classification rate is defined by adding any prerequisite, it is impossible to apply a conventional evaluation method to process data in many cases because process data has the particularity that the number of data values is small and the number of explanation variables is large. That is, a method for obtaining the information about the reliability and accuracy of a data mining result of process data is not established yet.
Therefore, it is necessary to develop an evaluation method applicable to a data mining result of process data or the like. Moreover, because an obtained data-mining result does not always show a true state, it is preferable to obtain the information about other possible factors as factors from a secondary factor downward. Furthermore, most data-mining algorithms conform to multivariate analysis and it is difficult to make an end user unfamiliar with a statistical method understand the analysis result. Therefore, an comprehensible criterion is necessary.
Furthermore, analysis of process data uses the history of a device used, test results, design information, and various measured data values as explanation variables as described above. However, the history of a device used, test results, design information, and various measured data values are data species included in different types of item groups (categories), i.e., data species of different type. In general, in the case of a conventional process-data analyzing method, it is difficult to separate or decrease influences of explanation variables included in another item group. Therefore, the relation with a yield value serving as a purpose variable is analyzed only for an explanation variable included in a signal item group. Therefore, obtained each analysis result relates to an explanation variable included in a signal item group.
For example, in the conventional analyzing method, when using an explanation variable as the history of a device used in each process, the influence on a yield due to a difference between devices in each process is only known. Moreover, when using an explanation variable as electrical-characteristic data, only the information showing influences of any electrical-characteristic data value on a yield is obtained. That is, in the conventional analyzing method, the information on the relation between explanation variables while lying across explanation variables of different item groups or included in different item groups cannot be obtained. Moreover, the relation between an analysis result of a certain item group and an analysis result of another item group or the information for the difference between influential degrees of explanation variables included in different item groups on purpose variables cannot be obtained.
Therefore, even if it is clarified by the conventional analyzing method that a difference between devices occurs, the influential degree of electrical characteristic data on a yield may be actually larger than influences of the difference between devices or the difference between devices may not actually occur compared to an analysis result obtained through noises. In this case, even if taking action for the difference between devices by referring to an analysis result of the history of a device used, the action is not very effective.
Particularly, recently, because a device or the like is further fined and data in the world is further complicated, failure factors due to design or fabrication factors are complexly interwound each other and the history of a device used, test results, design information, and various measured data values reflecting the above mentioned are not independent of each other but they are complexly interwound each other. Therefore, even if simply analyzing the influence on a yield value every item, an actual phenomenon is not always accurately shown.
Therefore, a data analyzing method and a data analyzing device are necessary which can perform analysis while lying across the data of different item groups and thereby obtain the fact that an explanation variable included in any item group and effective for a purpose variable under a state of less noises. However, there is not any method for obtaining the relation between explanation variables included in different item groups or for knowing how the explanation variables are interwound each other.
It is an object of the present invention to provide a data analyzing device and a data analyzing method capable of evaluating the reliability and accuracy of a data mining result of the process data or the like particularly obtained in a semiconductor fabrication process or capable of quantitatively evaluating effective factors from a secondary factor downward.
It is another object of the present invention to provide a data analyzing device and a data analyzing method capable of performing an analysis under a state of less noises by handling a plurality of items different from each other in belonging item group as explanation variables simultaneously in parallel and analyzing a set included or not included in a watched node of a regression tree diagram based on an extracted rule.
According to one aspect of the present invention, a data processing section extracts a rule present between a plurality of original data values of an original data group by to generate a reliability-information-provided rule file to which the information showing the reliability of the rule is added. The extracted rule is output together with the information showing the reliability of the rule. Then, the original data is analyzed in accordance with the rule file by an analyzing tool.
A statistical method such as a data mining technique is utilized for extracting the rule present between original data values. Moreover, a set-division evaluation value is obtained which shows the clearness of division when dividing a set constituted of a plurality of original data values into to two subsets. The information showing the reliability of the rule can also use the information including factors or conditions from a secondary factor or condition downward.
Moreover, the original data includes purpose variables purposing the search of fluctuation causes or fluctuation patterns and explanation variables for explaining the fluctuation of the purpose variables. When applying the present invention to a device for analyzing yield deterioration factors in a fabrication process, a purpose variable uses a fabrication yield. Moreover, explanation variables use the history of a device used, test results, design information, and measured data.
Moreover, an S-ratio is set as one of set-division evaluation values. When assuming the sum of squares of purpose variables before dividing a set constituted of a plurality of original data values into two subsets as S0 and the sums of squares of purpose variables of subsets after dividing as S1 and S2, the S-ratio is shown by the following equation (3).
S-ratio=((S1+S2)/2)/S0xe2x80x83xe2x80x83(3)
The S-ratio is a reduction rate of the sum of squares according to set division and a parameter showing a reduction rate of the sum of squares by set division. As the S-ratio decreases, the effect of set division increases. That is, because this represents that set division is clearly performed, a difference between devices increases.
Moreover, a t-value is set as one of set-division evaluation values. This value is used for the examination of the difference between averages of subsets after divided. When assuming the sums of squares of purpose variables of sets obtained by dividing a set constituted of a plurality of original data values into two subsets as S1 and S2, the numbers of factors of subsets after divided as N1 and N2, and averages of subsets after divided as /X1 and /X2 (symbol xe2x80x9c/xe2x80x9d before X denotes a bar), a t-value is shown by the following equations (4) and (4)xe2x80x2.                     t        =                              "LeftBracketingBar"                                          X1                _                            -                              X2                _                                      "RightBracketingBar"                                                                                S1                  +                  S2                                                  N1                  +                  N2                  -                  2                                            xc3x97                              (                                                      1                    N1                                    +                                      1                    N2                                                  )                                                                        (        4        )                                t        =                              "LeftBracketingBar"                                          X1                _                            -                              X2                _                                      "RightBracketingBar"                                                              S1                                  N1                  2                                            +                              S2                                  N2                  xe2x80x2                                                                                        (                  4          xe2x80x2                )            
Equation (4) is applied when there is no significant difference between variances of divided sets and equation (4)xe2x80x2 is applied when there is a significant difference between variances of divided sets.
A t-value is a value for examining the difference between two population means of sets respectively divided into two subsets and serves as a criterion showing a significant difference between average values of purpose variables of divided sets. When the same degree of freedom, that is, the same number of data values represents that a set is more clearly divided as a t-value increases and therefore, a difference between devices increases.
Moreover, it is allowed to use a configuration in which each record of original data has a plurality of items included in different types of a plurality of item groups as explanation variables and a set included or not included in a watched node of a regression tree diagram based on an extracted rule is analyzed.
According to the present invention, a reliability-information-provided rule file to which the information showing the reliability of a rule is added is generated in the rule present between a plurality of original data values of an original data group. The generated rule and the information showing the reliability are output. Then, original data is analyzed in accordance with the generated rule file. Therefore, it is possible to evaluate the accuracy of an extracted rule and obtain effective factors from a secondary factor downward together with quantitative evaluation values of the factors (S-ratio and t-value).
Moreover, according to the present invention, it is possible to obtain explanation variables influencing purpose variables while lying across different item groups together with reliability information by handling a plurality of items included in different item groups as explanation variables simultaneously and executing a regression tree analysis. As a result, it is possible to obtain the information showing the data of an item group influencing a purpose variable as an explanation variable.
Moreover, because an explanation variable located at a higher position on a regression tree diagram has a larger influential degree on a purpose variable, it is possible to perform an analysis under a state excluding the influential degree due to an item having an influential degree larger than that of the item of a watched node by analyzing a set included or not included in the watched node.
Furthermore, by analyzing original data excluding the data for a node lower than the watched node, it is possible to perform an analysis under a state excluding the influential degree of an item having an influential degree smaller than that of the item of the watched node.
Other objects and features of this invention will become apparent from the following description with reference to the accompanying drawings.